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Reference Angles definitions

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  • Reference Angle
    Smallest positive angle formed between a given angle's terminal side and the nearest x-axis, always corresponding to a quadrant 1 angle.
  • Unit Circle
    A circle centered at the origin with radius 1, used to define trigonometric values for all angles.
  • Quadrant
    One of four sections of the coordinate plane, each determining the sign of trigonometric values.
  • Coterminal Angle
    Angles sharing the same terminal side, differing by full rotations of 360° or 2π radians.
  • Terminal Side
    The position of a ray after rotation from the initial side, used to determine angle placement.
  • Initial Side
    The starting position of a ray before rotation, typically along the positive x-axis.
  • Sine
    Trigonometric function representing the y-coordinate of a point on the unit circle.
  • Cosine
    Trigonometric function representing the x-coordinate of a point on the unit circle.
  • Tangent
    Trigonometric function found by dividing sine by cosine, or y-coordinate by x-coordinate.
  • Radian
    Angle measure based on arc length, where 2π radians equals a full circle.
  • Sign Convention
    Rule determining whether trigonometric values are positive or negative based on quadrant location.
  • ASTC Mnemonic
    Phrase 'All Students Take Calculus' used to remember which trigonometric functions are positive in each quadrant.
  • Full Rotation
    A complete turn around the circle, equal to 360 degrees or 2π radians.
  • X-Axis
    Horizontal axis in the coordinate plane, used as a reference for measuring angles.
  • Y-Axis
    Vertical axis in the coordinate plane, used to determine the sign of sine values.